Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the values of the variable can be less than or equal to a certain number.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the values of the variable can be greater than or equal to a certain number.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed or solid line. 2. Use a dashed line for < or > (not including the line) and a solid line for ≤ or ≥ (including the line). 3. Shade the region that satisfies the inequality.

Front

What is the difference between '>' and '≥'?

Back

'>' means 'greater than' and does not include the boundary line, while '≥' means 'greater than or equal to' and includes the boundary line.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality. It is represented by the shaded region on the graph.

Front

How do you determine which side of the line to shade when graphing a linear inequality?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0)). Substitute the coordinates into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.

Front

What is the inequality for the line with slope -2 and y-intercept -2?

Back

Front

What is the inequality for the vertical line x = 2?

Back

Front

What does it mean if a point (4, -2) is a solution to a linear inequality?

Back

It means that when you substitute x = 4 and y = -2 into the inequality, the statement is true, indicating that the point lies in the shaded region of the graph.